I have the same machine, have to made the video about sorting the back lash on that cross feed. Mine about 5 mm. Do not think it is only the nut because the pitch is about 5 mm. Perhaps a spacer is missing. What about to modify the nut to take up the small free play as it wears. Like you mentions all the chips gets blown on to the lead screw and then that keyway acts like a cutter.

Also like your DRO set-up. Is it on the chuck side. Where did you get it and what make is it? Looks and sounds like you from ZAR.